f.4 數學 (ENG) (URGENT!)

[匿名]

2010-08-03 1:25 am

1. In the figure, O is the centre of the circle. AB = 4cm. ON is 3cm. OM is 1cm.
Find the length of CD,
http://yfrog.com/0j41968527p

2. ABCD is a parallelogram in which AC= 7cm and BD=10cm. The diagonals AC and BD intersect at K and angle BKC=74degree. Find its area.
http://img340.imageshack.us/i/70291976.png/

Please show the steps. THZ

更新1:

3. tan (45degrees+A) tan(45degrees-A) I know the ans is 1. But could you show me the steps?

更新2:

陽光: 你好, 請問, 第1題你怎知 ANGLE ANO 是直角啊?

更新3:

☂雨後陽光☀ 不好意思, 可否回答我最後一題, 無論回答與否, 我也俾最佳你的! 4. In the figure, AC is a diameter and angleBAC =angle CAD. Show that AD=AB. http://yfrog.com/2c85789528p

回答 (1)

用戶2053

2010-08-03 1:57 am

✔ 最佳答案

1)OA^2 = ON^2 + AN^2OA^2 = 3^2 + (4/2)^2OA^2 = 13Since OC = OA = radius ,OC^2 = 13 OM^2 + CM^2 = 131^2 + (CD/2)^2 = 13(CD/2)^2 = 12CD^2 = 48CD = √ (3*16)CD = 4 √ 3 cm
2)Since AK = CK , BK = DK (prop. of //gram)Area of △BKC = △CKD = △DKA = △AKBRequired Area = 4 * △BKC= 4 * (1/2) BK * CK * sin74°= 4 * (1/2) (10/2) (7/2) sin74°= 35 sin74°= 33.644 cm^2
3)tan (45° + A) tan(45°- A)= tan (45°+A) tan (90° - (45°+A) )= tan (45°+A) [ 1 / tan (45°+A) ] ....... Formula : tan (90° - x) = 1 / tan x= 1

2010-08-02 19:42:36 補充：
題目的確無話ANGLE ANO , OMC是直角。

但這樣應該無得計, CD 因與 OM 角度不同而長短不同。

2010-08-02 22:05:28 補充：
4)

連BC , DC , 因AC為直徑 , ㄥABC = ㄥADC = 90° ,

又已知ㄥABC = ㄥCAD ,

故ㄥACB = ㄥACD ,

即 AB = AD (等角等弦)

Thanks you !!

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